Trait-mediated speciation and human-driven extinctions in proboscideans revealed by unsupervised Bayesian neural networks

Species life-history traits, paleoenvironment, and biotic interactions likely influence speciation and extinction rates, affecting species richness over time. Birth-death models inferring the impact of these factors typically assume monotonic relationships between single predictors and rates, limiting our ability to assess more complex effects and their relative importance and interaction. We introduce a Bayesian birth-death model using unsupervised neural networks to explore multifactorial and nonlinear effects on speciation and extinction rates using fossil data. It infers lineage- and time-specific rates and disentangles predictor effects and importance through explainable artificial intelligence techniques. Analysis of the proboscidean fossil record revealed speciation rates shaped by dietary flexibility and biogeographic events. The emergence of modern humans escalated extinction rates, causing recent diversity decline, while regional climate had a lesser impact. Our model paves the way for an improved understanding of the intricate dynamics shaping clade diversification.

The PDF file includes: Figs. S1 to S8 Tables S1 to S3 Legends for data S1 and S2 Other Supplementary Material for this manuscript includes the following:

Data S1 and S2
Supplementary figures To assess the performance of the BDNN model, we specified e ight s cenarios w here s peciation a nd extinctions r ate: ( A) a re c onstant through time and independent of species' traits, (B) change over time according to a logistic function, (C) shift instantaneously at discrete moments in time, (D) depend on two states of a categorical trait that determine whether rates are a bell-shaped or inverted bell-like function of paleotemperature, (E) approach a state-dependent equilibrium due to an increase in extinction over time, (F) are defined b y a n on-monotonic f unction o f a c ontinuous t rait, ( G) w ill show a bell-shaped or inverted bell-like relationship with a continuous trait, depending on the state of a categorical trait, or (H) change from a inverted bell-shaped function of a continuous trait to a bell-shaped relationship at 15 Ma.All simulated datasets include additional traits and time-dependent variables that did not influence speciation and extinction r ates.For scenario 9, where the influential trait is missing, we used the data of scenario 6 and replaced the continuous trait with a random draw from a standard normal distribution.All rates are given in units of events • lineage −1 Fig. S2.Sensitivity to find evidence of rate variation among species and over time.For simulated diversification scenarios where speciation and extinction rates varied as a function of traits and time-dependent variables, we quantified the coefficient of variation in inferred lineage-specific rates and calculated over 100 thresholds the proportion of correctly evidenced rate heterogeneity.The dashed vertical line displays the threshold of 0.16 for speciation and 0.14 for extinction to detect rate variation. .Simulated and inferred variation in lineage-time-specific rates.Coefficient of variation (CV) in (A) speciation and (B) extinction rate across all species was calculated in each of the 100 simulation replicates under eight scenarios of diversification depending on traits and time-dependent variables.The dashed horizontal lines display the thresholds for speciation and extinction above which a constant rate model was rejected with 95% specificity.The simulated speciation rate was taken from the ancestral lineage from which the species branch off and whose rates are inferred.Regularization parameter t reg for (C) speciation and (D) extinction rate shows the degree of shrinking lineage-time-specific rates to a common mean in the neural network.Rates are constant when t reg = 0 and not shrank when t reg ≈ 1. Fig. S5.Power to identify rate predictors.Barplots show the result of three individual metrics from explainable artificial intelligence and their consensus.Solid colors display the proportion when a simulated effect of traits and time-dependent variables on speciation and extinction rates was actually ranked as the most influential ( Predictor 1 ) d uring t he B DNN inference, among the top two (Predictor 2) when one rate determinant alters the effect of another, or in case of scenario 9 phylogenetic relatedness identified i nstead o f a n o mitted i nfluential trait.
The share of a two-way interaction being identified as the most important is indicated by the hatched pattern (Interaction).Total height of the barplots equals the number of simulations that exceed our threshold to reject the constant rate model.Solid lines display the mean and the shaded interval the 75% and 95% credible interval.The y-axis of the extinction and net-diversification rate is compressed for values greater than 1.0 and smaller than 0.5, respectively, to aid rate comparison before the Holocene extinction peak.All rates are marginal rates, which were inferred with the BDNN model for all species that are extant in pre-defined time windows and are given in units of of events • lineage −1 • myr −1 .The diversity trajectory shows the range-through richness from the times of origin and extinction of all species that were inferred together with the speciation and extinction rates.Species-times specific rates inferred for 175 proboscidean species based on 11 predictors (plus humans for extinction) plotted against a simpler BDNN model based on 6 predictors (plus humans for extinction).Circles represent the posterior mean rate, while the whiskers represent the 95% CI.The rates were considered consistent when the mean rate under the simpler model fell within the 95% CI of the more complex model.Speciation and extinction rates were consistent across 98% of the species, indicating that the models converge onto similar results overall.
Fig.S1.Simulated diversification scenarios.To assess the performance of the BDNN model, we specified e ight s cenarios w here s peciation a nd extinctions r ate: ( A) a re c onstant through time and independent of species' traits, (B) change over time according to a logistic function, (C) shift instantaneously at discrete moments in time, (D) depend on two states of a categorical trait that determine whether rates are a bell-shaped or inverted bell-like function of paleotemperature, (E) approach a state-dependent equilibrium due to an increase in extinction over time, (F) are defined b y a n on-monotonic f unction o f a c ontinuous t rait, ( G) w ill show a bell-shaped or inverted bell-like relationship with a continuous trait, depending on the state of a categorical trait, or (H) change from a inverted bell-shaped function of a continuous trait to a bell-shaped relationship at 15 Ma.All simulated datasets include additional traits and time-dependent variables that did not influence speciation and extinction r ates.For scenario 9, where the influential trait is missing, we used the data of scenario 6 and replaced the continuous trait with a random draw from a standard normal distribution.All rates are given in units of events • lineage −1 • myr −1 .
Fig.S3.Simulated and inferred variation in lineage-time-specific rates.Coefficient of variation (CV) in (A) speciation and (B) extinction rate across all species was calculated in each of the 100 simulation replicates under eight scenarios of diversification depending on traits and time-dependent variables.The dashed horizontal lines display the thresholds for speciation and extinction above which a constant rate model was rejected with 95% specificity.The simulated speciation rate was taken from the ancestral lineage from which the species branch off and whose rates are inferred.Regularization parameter t reg for (C) speciation and (D) extinction rate shows the degree of shrinking lineage-time-specific rates to a common mean in the neural network.Rates are constant when t reg = 0 and not shrank when t reg ≈ 1.
Fig.S4.Simulated versus inferred rates.Under eight scenarios A-H (see Fig.S1), true speciation and extinction rates (dashed lines) were a function of traits and time-dependent variables and used to simulate 100 fossil datasets for each scenario.Transparent lines show partial-dependence (PD) rates calculated from the inferred BDNN model and the thick solid line represents the average across them after locally estimated scatterplot smoothing (loess).Each simulated dataset subjected to the BDNN inference contained complementary traits, phylogenetic eigenvectors, or time-dependent variables that did not influenced diversification and the PD rates display the exclusive influence of the focal traits and variables by marginalizing over the complementary ones.All rates are given in units of events • lineage −1 • myr −1 .
Fig.S6.Proboscidean diversification through time.Shown are (A) speciation rate, (B) extinction rate, (C) net-diversification, and (D) diversity across 10 replicates, incorporating the dating uncertainty of the fossil record.Solid lines display the mean and the shaded interval the 75% and 95% credible interval.The y-axis of the extinction and net-diversification rate is compressed for values greater than 1.0 and smaller than 0.5, respectively, to aid rate comparison before the Holocene extinction peak.All rates are marginal rates, which were inferred with the BDNN model for all species that are extant in pre-defined time windows and are given in units of of events • lineage −1 • myr −1 .The diversity trajectory shows the range-through richness from the times of origin and extinction of all species that were inferred together with the speciation and extinction rates.
Fig.S7.Influence of regional paleotemperature on proboscidean extinction.Partial dependence plot showing the effect of paleotemperature on extinction rate.Solid lines display the mean partial dependence rate and the shaded interval the 75% and 95% credible interval.Ticks along the x-axis indicate the temperature at the inferred time of proboscidean extinction or the present-day value for the three extant elephant species.Extinction rate is given in units of of events • lineage −1 • myr −1 .